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Step-by-Step Solution
Step 1: Understand the Relationship
Conductivity (commonly denoted by K ) is related to the cell constant and the measured resistance of the electrolytic solution by the equation:
K = \dfrac{\text{Cell Constant}}{R},
which can be rearranged as:
\text{Cell Constant} = K \times R.
Step 2: Gather the Known Values
Resistance, R = 1750\,\Omega
Conductivity, K = 0.152 \times 10^{-3}\,\text{S cm}^{-1}
Step 3: Substitute the Values into the Formula
Using \text{Cell Constant} = K \times R :
\text{Cell Constant}
= (0.152 \times 10^{-3}\,\text{S cm}^{-1})
\times (1750\,\Omega).
Step 4: Perform the Calculation
First, convert 0.152 \times 10^{-3} to a decimal:
0.152 \times 10^{-3}
= 0.000152.
Now multiply 0.000152 by 1750 :
0.000152 \times 1750
= 0.266.
Step 5: State the Result
The cell constant of the conductivity cell is:
\text{Cell Constant} = 0.266\,\text{cm}^{-1}.
Alternatively, you can write:
0.266\,\text{cm}^{-1}
= 266 \times 10^{-3}\,\text{cm}^{-1}.
